What do you know about the link between artwork and mathematics? Mention some examples.
So we know that mathematics are everywhere, as artwork are not the exception. In many artworks we can find the golden ratio, the golden rectangle and golden spiral.
The golden ratio can be found in "El hombre de Vitrubio" by Leonardo Da Vinci.
The golden rectangle can be found in "La Gioconda" by Leonardo Da Vinci and
The golden spiral can be found in "Semitaza gigante volando con anexo inexplicable de cinco metros de longitud" by Salvador Dalí.
During Reading and After Reading
1. Please click on the following link to read the article.
3. Please write what the following referents (in bold letters) refer to in the text:
Mathematicians often rhapsodize about the austere elegance of a well-wrought proof. But math also has a simpler sort of beauty that is perhaps easier to appreciate...
That refers to "a simpler sort of beauty"
That beauty was richly on display at an exhibition of mathematical art at the Joint Mathematics Meeting in San Diego in January, where more than 40 artists showed their creations.
Where refers to "Joint Mathematics Meeting in San Diego"
A mathematical dynamical system is just any rule that determines how a point moves around a plane. Field uses an equation that takes any point on a piece of paper and moves it to a different spot. Field repeats this process over and over again—around 5 billion times—and keeps track of how often each pixel-sized spot in the plane gets landed on. The more often a pixel gets hit, the deeper the shade Field colors it.
It refers to "any point"
This process refers to "moves any point to a different spot"
It refers to "a pixel"
The reason mathematicians are so fascinated by dynamical systems is that very simple equations can produce very complicated behavior. Field has found that such complex behavior can create some beautiful images.
Such complex behavior refers to "field"
Robert Bosch, a mathematics professor at Oberlin College in Ohio, took his inspiration from an old, seemingly trivial problem that hides some deep mathematics. Take a loop of string and throw it down on a piece of papaer. It can form any shape you like as long as the string never touches or crosses itself. A theorem states that the loop will divide the page into two regions, one inside the loop and one outside.
His refers to "Robert Bosch"
That refers to "Trivial problem"
It refers to "a loop of string"
Itself refers to "string"
One inside refers to "region one of loop"
One outside refers to "region two of loop"
It is hard to imagine how it could do anything else, and if the loop makes a smoothly curving line, a mathematician would think that is obvious too. But if a line is very, very crinkly, itmay not be obvious whether a particular point lies inside or outside the loop. Topologists, the type of mathematicians who study such things have managed to construct many strange, "pathological" mathematical objects with very surprising properties, so they know from experience that you shouldn't assume a proof is unnecessary in cases like this one.
It refers to "the curving line"
Who refers to "Topologists"
You refers to "each person who reads the text"
This one refers to "this case (the loop makes a smoothly curving line)"
After reading the text, please answer the following questions in your own words:
4. Where did Robert Bosch take his inspiration from? Describe the source of his inspiration.
The inspiration of Robert Bosch from an old, seemingly trivial problem that hides some deep mathematics.
5. What happened with Fathauer's arrangement? Why?
The arrangement of Fathauer surprising is that he was just playing with various forms without noticing that what he was doing would result the triangle Sierpinski. The shape was approximating a pyramid, with triangular holes punched out.
6. How did Andrew Pike create the Sierpinski carpet? " To create a Sierpinski carpet, take a square, divide it in a tic-tac-toe pattern, and take out the middle square. Then draw a tic-tac-toe pattern on each remaining square and knock out the middle squares of those. Continuing forever will create the Sierpinski carpet "
7. Why did he choose that image?
Andrew Pike says: "We chose the image of Sierpinski because it was self-referential". "Seems appropiate for a technique using self-similar fractals".
Super 7pts
Reading Log 2 - Math on Display. Visualizations of mathematics create remarkable artwork
Pre-Reading
Read the title and write a list of ten words you think you might find in the text.
art, artist, sculpture, picture, paint, formula, projection, lines, angles, matter, mathematical.
What do you know about the link between artwork and mathematics? Mention some examples.
So we know that mathematics are everywhere, as artwork are not the exception. In many artworks we can find the golden ratio, the golden rectangle and golden spiral.The golden ratio can be found in "El hombre de Vitrubio" by Leonardo Da Vinci.
The golden rectangle can be found in "La Gioconda" by Leonardo Da Vinci and
The golden spiral can be found in "Semitaza gigante volando con anexo inexplicable de cinco metros de longitud" by Salvador Dalí.
During Reading and After Reading
1. Please click on the following link to read the article.
http://www.sciencenews.org/view/generic/id/9383/title/Math_on_Display
2. While reading, please locate the words you listed in the pre-reading and write a list of the ones you found in the text
art, artists, picture, line, triangle, mathematical.
3. Please write what the following referents (in bold letters) refer to in the text:
That refers to "a simpler sort of beauty"
- That beauty was richly on display at an exhibition of mathematical art at the Joint Mathematics Meeting in San Diego in January, where more than 40 artists showed their creations.
Where refers to "Joint Mathematics Meeting in San Diego"- A mathematical dynamical system is just any rule that determines how a point moves around a plane. Field uses an equation that takes any point on a piece of paper and moves it to a different spot. Field repeats this process over and over again—around 5 billion times—and keeps track of how often each pixel-sized spot in the plane gets landed on. The more often a pixel gets hit, the deeper the shade Field colors it.
It refers to "any point"This process refers to "moves any point to a different spot"
It refers to "a pixel"
- The reason mathematicians are so fascinated by dynamical systems is that very simple equations can produce very complicated behavior. Field has found that such complex behavior can create some beautiful images.
Such complex behavior refers to "field"- Robert Bosch, a mathematics professor at Oberlin College in Ohio, took his inspiration from an old, seemingly trivial problem that hides some deep mathematics. Take a loop of string and throw it down on a piece of papaer. It can form any shape you like as long as the string never touches or crosses itself. A theorem states that the loop will divide the page into two regions, one inside the loop and one outside.
His refers to "Robert Bosch"That refers to "Trivial problem"
It refers to "a loop of string"
Itself refers to "string"
One inside refers to "region one of loop"
One outside refers to "region two of loop"
It is hard to imagine how it could do anything else, and if the loop makes a smoothly curving line, a mathematician would think that is obvious too. But if a line is very, very crinkly, it may not be obvious whether a particular point lies inside or outside the loop. Topologists, the type of mathematicians who study such things have managed to construct many strange, "pathological" mathematical objects with very surprising properties, so they know from experience that you shouldn't assume a proof is unnecessary in cases like this one.
It refers to "the curving line"
Who refers to "Topologists"
You refers to "each person who reads the text"
This one refers to "this case (the loop makes a smoothly curving line)"
After reading the text, please answer the following questions in your own words:
1. What is a mathematical dynamical System?Is just any rule that determines how a point moves around a plane. Field uses an equation that takes any point on a piece of paper and moves it to a different spot
2. Why does the image "Coral Star" get more and more complex?
The reason is that very simple equations can produce very complicated behavior. Field has found that such complex behavior can create some beautiful images. In"Coral Star" does some peculiar things as it gets closer to the center (technically, the equation is discontinuous at the origin).
3. Find a definition of the following words that fits in the text, please acknowledge the source:
Loop, crinckly, string
Loop : A sequence of instructions that repeats either a specified number of times or until a particular condition is met.http://www.answers.com/topic/loop
Crinckly: any of several virus diseases of plants marked by crinkling of leaves.http://www.merriam-webster.com/dictionary/crinkly
String: A thread or cord on which a number of objects or parts are strung or arranged in close and orderly succession; hence, a line or series of things arranged on a thread, or as if so arranged; a succession; a concatenation; a chain; as, a string of shells or beads; a string of dried apples; a string of houses; a string of arguments. http://ardictionary.com/String/16680
4. Where did Robert Bosch take his inspiration from? Describe the source of his inspiration.
The inspiration of Robert Bosch from an old, seemingly trivial problem that hides some deep mathematics.
5. What happened with Fathauer's arrangement? Why?
The arrangement of Fathauer surprising is that he was just playing with various forms without noticing that what he was doing would result the triangle Sierpinski. The shape was approximating a pyramid, with triangular holes punched out.
6. How did Andrew Pike create the Sierpinski carpet?
" To create a Sierpinski carpet, take a square, divide it in a tic-tac-toe pattern, and take out the middle square. Then draw a tic-tac-toe pattern on each remaining square and knock out the middle squares of those. Continuing forever will create the Sierpinski carpet "
7. Why did he choose that image?
Andrew Pike says: "We chose the image of Sierpinski because it was self-referential". "Seems appropiate for a technique using self-similar fractals".